Functions and Linearity

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Tags

CCSS.8.F.A.1

Front

Which of the following sets of values is a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function because each first element (x-value) is unique.

Tags

CCSS.8.F.A.1

Front

Is the equation y = 4x^4 + 8 a linear function?

Back

No, it is a nonlinear function because it contains a variable raised to a power greater than 1.

Tags

CCSS.8.F.A.3

Front

What characterizes a linear function?

Back

A linear function is characterized by a constant rate of change and can be represented by a straight line on a graph.

Tags

CCSS.HSF-LE.A.1B

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed, often involving variables raised to powers other than one or involving products of variables.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by a straight line on the graph.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and graphs as a curve.

Tags

CCSS.8.F.A.3